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Math  /  Numbers & Operations

QuestionEnglis Converting a Percent to a Decimal \begin{tabular}{|l|l|l|l|l|l|l|l|l|l|} \hline & & & & & & & & & \\ \hline & & & & & & & & & \\ \hline & & & & & & & & & \\ \hline & & & & & & & & & \\ \hline & & & & & & & & \\ \hline & & & & & & & & & \\ \hline & & & & & & & & & \\ \hline & & & & & & & & & \\ \hline & & & & & & & & & \\ \hline & & & & & & & & & \\ \hline & & & & & & & & & \\ \hline & & & & & & & & & \\ \hline \end{tabular}
What percent of the model is shaded? □\square What is the equivalent ratio? □\square What is the equivalent decimal? □\square What is the equivalent fraction? □\square

Studdy Solution

STEP 1

1. The grid is a 10x10 grid, which means there are 100 total squares.
2. 70 out of the 100 squares are shaded.
3. We need to convert this information into a percent, ratio, decimal, and fraction.

STEP 2

1. Calculate the percent of the model that is shaded.
2. Determine the equivalent ratio.
3. Convert the percent to a decimal.
4. Express the shaded portion as a fraction.

STEP 3

Calculate the percent of the model that is shaded using the formula: Percent Shaded=(Number of Shaded SquaresTotal Number of Squares)×100 \text{Percent Shaded} = \left( \frac{\text{Number of Shaded Squares}}{\text{Total Number of Squares}} \right) \times 100
Percent Shaded=(70100)×100=70% \text{Percent Shaded} = \left( \frac{70}{100} \right) \times 100 = 70\%

STEP 4

Determine the equivalent ratio by comparing the number of shaded squares to the total number of squares. Equivalent Ratio=Number of Shaded SquaresTotal Number of Squares=70100 \text{Equivalent Ratio} = \frac{\text{Number of Shaded Squares}}{\text{Total Number of Squares}} = \frac{70}{100} This ratio can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 10. Equivalent Ratio=70÷10100÷10=710 \text{Equivalent Ratio} = \frac{70 \div 10}{100 \div 10} = \frac{7}{10}

STEP 5

Convert the percent to a decimal by dividing by 100. Equivalent Decimal=70100=0.70 \text{Equivalent Decimal} = \frac{70}{100} = 0.70

STEP 6

Express the shaded portion as a fraction, which was already calculated in the ratio step. Equivalent Fraction=70100=710 \text{Equivalent Fraction} = \frac{70}{100} = \frac{7}{10}
Solution:
1. Percent of the model that is shaded: 70%70\%
2. Equivalent ratio: 710\frac{7}{10}
3. Equivalent decimal: 0.700.70
4. Equivalent fraction: 710\frac{7}{10}

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